1. Field of the Invention
The invention relates to a rotation angle detection apparatus that detects a rotation angle of a rotor.
2. Description of Related Art
A brushless motor that is used in, for example, an electric power steering system is controlled by supplying currents to stator coils in accordance with the rotation angle of a rotor. For example, rotation angle detection apparatuses, such as the one illustrated in FIGS. 3A and 3B, are known. The illustrated rotation angle detection apparatus includes a detection rotor 1 that rotates as a rotor of a brushless motor rotates, and two magnetic sensors 11 and 12 that are arranged apart from each other at an angular interval of 90° about the rotation axis of the detection rotor 1. The detection rotor 1 includes two magnets 2 each of which has two magnetic poles. The magnetic sensors 11 and 12 output sinusoidal signals of which the phases are different from each other by 90°. The rotation angle of the detection rotor 1 is detected based on the two sinusoidal signals (for example, refer to Japanese Patent Application Publication No. 06-109750 (JP 06-109750 A) and Japanese Patent Application Publication No. 2008-283762 (JP 2008-283762 A)).
The arrow in FIG. 3A indicates the normal rotation direction of the detection rotor 1. As the detection rotor 1 rotates in the normal rotation direction, the rotation angle of the detection rotor 1 increases. On the other hand, as the detection rotor 1 rotates in the reverse rotation direction, the rotation angle of the detection rotor 1 decreases. If the rotation angle (electric angle) of the detection rotor 1 is θ, an output signal V1 of the first magnetic sensor 11 (will hereinafter be referred to as “the first output signal V1”), which is one of the two magnetic sensors, is expressed as V1=A1·sin θ, and an output signal V2 of the second magnetic sensor 12 (will hereinafter be referred to as “the second output signal V2”), which is the other of the two magnetic sensors, is expressed as V2=A2·sin(θ+90°)=A2·cos θ. In these equations, A1 and A2 each represent an amplitude.
If the amplitudes A1 and A2 are both regarded as a prescribed value A, or if the first and second output signals V1 and V2 are normalized such that the amplitudes A1 and A2 both become the prescribed value A, the first output signal V1, which is one of the two output signals, is expressed as V1=A·sin θ, and the second output signal V2, which is the other of the two output signals, is expressed as V2=A·cos θ. Further, if A is 1, the first output signal V1 is expressed as V1=sin θ and the second output signal V2 is expressed as V2=cos θ. Thus, for simpler descriptions, the first output signal V1 of the first magnetic sensor 11 and the second output signal V2 of the second magnetic sensor 12 will be expressed as V1=sin θ and V2=cos θ, respectively. FIG. 4 is a graph illustrating the waveforms of the first and second output signals V1 and V2.
The rotation angle θ of the rotor 1 is determined using the first and second output signals V1 and V2, according to, for example, Equation 1 shown below.
                                                        θ              =                            ⁢                                                tan                                      -                    1                                                  ⁡                                  (                                      sin                    ⁢                                                                                  ⁢                                          θ                      /                      cos                                        ⁢                                                                                  ⁢                    θ                                    )                                                                                                        =                            ⁢                                                tan                                      -                    1                                                  ⁡                                  (                                      V                    ⁢                                                                                  ⁢                                          1                      /                      V                                        ⁢                                                                                  ⁢                    2                                    )                                                                                        Equation        ⁢                                  ⁢        1            
In the conventional rotation angle detection apparatus as described above, if the gap between the first magnetic sensor 11 and the rotor 1 and the gap between the second magnetic sensor 12 and the rotor 1 are small, third harmonic components are superimposed on the first output signal V1 of the first magnetic sensor 11 and the second output signal V2 of the second magnetic sensor 12, causing distortion of the waveforms of the first and second output signals V1 and V2. For example, as shown in FIG. 5, the smaller the gap D (refer to FIG. 3B) between the first magnetic sensor 11 and the detection rotor 1, the larger the distortion of the first output signal V1 of the first magnetic sensor 11. In a case where the first output signal V1 of the first magnetic sensor 11 and the second output signal V2 of the second magnetic sensor 12 are distorted as in this example case, the rotation angle θ calculated based on the first and second output signals V1 and V2 may have a calculation error.